How to join this arc
Use Spin tool and create the arc-shaped top based on the existing geometry.


Select top vertices which should serve as a base for the arc. Snap cursor to them with Shift+S menu. Note that spinning will happen based on 3D cursor position and the current orientation of the view in the viewport. 
Deselect one of the vertices leaving only one selected (to make spin happen from one origin).
Press Alt+R to execute the tool (or find it on the Toolshelf). Adjust Angle in operator's options to 180 degrees and set amount of steps according to your mesh.
Make sure to remove double vertices with W menu.